by Hening Huang
This paper presents two simple and practical frequentist methods for combining prior information with current measurement in uncertainty analysis. The first method is based on the “law of combination of distributions” (LCD). The second method is based on the least-squares principle. We focus on a problem that is often encountered in practice: the prior information is available from historical measurements and the current measurement gives a series of observations. Under the assumption of normality, both the LCD-based and least-squares methods give the same results. The philosophical and methodological difference between the LCD-based method and the Bayesian approach is discussed. This paper also presents a simple test to determine whether prior information is valid. If prior information is invalid, it should not be incorporated into current measurement because otherwise it would deteriorate the quality of the estimation of the measurand. Four examples are presented to demonstrate the effectiveness of the proposed frequentist methods, compared with their Bayesian counterparts.
